The use of a third platen on a thermoforming machine is known in order to more quickly advance an array of plugs into female mold cavities of a thermoforming machine. One machine uses a plurality of ball screws. Another machine uses a single roller screw shaft. Both machines provide a compromise between providing sufficient torque, or forming pressure, and providing a sufficiently fast stroke. Improvements are needed in order to provide both sufficient torque and sufficiently fast stroke in order to optimize article formation and surface finish.